GATE · Practice Sheet 30

1. 1.

   Mathematics

   If f(x) = 3x³ + 3x² + 8x, find f′(1).

   Formula:Derivative of a Polynomial

   $\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$

   View formula →
2. 2.

   Quantitative Aptitude

   Find the HCF and LCM of 15 and 36.

   Formula:LCM & HCF

   $\text{LCM}\times\text{HCF} = a\times b$

   View formula →
3. 3.

   Mathematics

   Evaluate log base 2 of 64.

   Formula:Logarithm Evaluation

   $\log_{b}(b^{k}) = k$

   View formula →
4. 4.

   Mathematics

   Find term number 7 of a geometric progression with first term 6 and common ratio 2.

   Formula:GP nth Term

   $a_n = a\,r^{\,n-1}$

   View formula →
5. 5.

   Physics

   A constant force of 73 N moves an object 30 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

   View formula →
6. 6.

   Quantitative Aptitude

   Find the HCF and LCM of 26 and 37.

   Formula:LCM & HCF

   $\text{LCM}\times\text{HCF} = a\times b$

   View formula →
7. 7.

   Mathematics

   Find term number 5 of a geometric progression with first term 6 and common ratio 2.

   Formula:GP nth Term

   $a_n = a\,r^{\,n-1}$

   View formula →
8. 8.

   Quantitative Aptitude

   A vehicle covers 170 km in 2 hours. Find its average speed.

   Formula:Speed, Distance & Time

   $\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$

   View formula →
9. 9.

   Quantitative Aptitude

   What is 75% of 380?

   Formula:Percentage of a Number

   $\text{Value} = \dfrac{P}{100}\times N$

   View formula →
10. 10.

    Quantitative Aptitude

    In how many ways can 3 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 3.)

    Formula:Combinations

    $^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$

    View formula →
11. 11.

    Physics

    Find the kinetic energy of a 9 kg object moving at 5 m/s.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2}mv^{2}$

    View formula →
12. 12.

    Mathematics

    Evaluate log base 2 of 32.

    Formula:Logarithm Evaluation

    $\log_{b}(b^{k}) = k$

    View formula →
13. 13.

    Quantitative Aptitude

    Find the simple interest on ₹34,000 at 5% per annum for 6 year(s).

    Formula:Simple Interest

    $SI = \dfrac{P\times R\times T}{100}$

    View formula →
14. 14.

    Mathematics

    Find the distance between the points (5, -2) and (5, -4).

    Formula:Distance Between Two Points

    $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

    View formula →
15. 15.

    Physics

    Find the electrical power when 40 V drives a current of 9 A.

    Formula:Electrical Power

    $P = VI$

    View formula →
16. 16.

    Mathematics

    Find the sum of the first 19 terms of an AP with first term 20 and common difference 1.

    Formula:AP Sum of n Terms

    $S_n = \dfrac{n}{2}\,[2a+(n-1)d]$

    View formula →
17. 17.

    Physics

    A projectile is launched at 14 m/s at 60° to the horizontal. Find its range (g = 9.8 m/s²).

    Formula:Projectile Range

    $R = \dfrac{u^{2}\sin 2\theta}{g}$

    View formula →
18. 18.

    Physics

    Find the kinetic energy of a 20 kg object moving at 5 m/s.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2}mv^{2}$

    View formula →
19. 19.

    Mathematics

    If f(x) = 3x³ + 3x² + 1x, find f′(5).

    Formula:Derivative of a Polynomial

    $\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$

    View formula →
20. 20.

    Quantitative Aptitude

    What is 60% of 380?

    Formula:Percentage of a Number

    $\text{Value} = \dfrac{P}{100}\times N$

    View formula →

© FormulaWon — formulawon.app · Answers & step-by-step working available on the solutions sheet.